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I was reading about the Callan Symanzik equation from Peskin and Schroeder. On page 411, they assume that since $G^{(n)}$, the connected Green's function is renormalized, the $\beta$ and $\gamma$ functions cannot depend on the cutoff $\Lambda$. Why is this so?

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  • $\begingroup$ Good question and good to doubt +1, but you may need to provide more detail discussions. and include the formulas, etc $\endgroup$ – wonderich Dec 23 '19 at 3:15
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As explained in the book, the Green's function has already been renormalised and thus the dependence on the regulator (whatever it is) dropped. In fact, nothing in the l.h.s. of Eq. (12.41)depends on the regulator. Hope this helps.

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